Problem: Let $f(x) = -4x^{2}+4x+7$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Explanation: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-4x^{2}+4x+7 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -4, b = 4, c = 7$ $ x = \dfrac{-4 \pm \sqrt{4^{2} - 4 \cdot -4 \cdot 7}}{2 \cdot -4}$ $ x = \dfrac{-4 \pm \sqrt{128}}{-8}$ $ x = \dfrac{-4 \pm 8\sqrt{2}}{-8}$ $x =\dfrac{-1 \pm 2\sqrt{2}}{-2}$